What if the Crusaders do not fight Saladin, but focus on strengthening their presence in the Outremer?
I am not saying they should abandon the goal of fighting the Muslims entirely (hopefully in the ATL future), but they don't confront Saladin.
With a good, wise leader of the Crusade, who focuses on religion and safety of the pilgrims and not war, even an alliance and/or "going native" are possible (remember, the Crusaders respected Saladin for his chivalry and wisdom).